group vs radical what difference

what is difference between group and radical

English

Alternative forms

  • groop (non-standard)
  • groupe (obsolete)

Etymology

From French groupe (cluster, group), from Italian gruppo, groppo (a knot, heap, group, bag (of money)), from Vulgar Latin *cruppo, Renaissance Latin grupus, from Proto-Germanic *kruppaz (lump, round mass, body, crop), from Proto-Indo-European *grewb- (to crumple, bend, crawl). Cognate with German Kropf (crop, craw, bunch), Old English cropp, croppa (cluster, bunch, sprout, flower, berry, ear of corn, crop), Dutch krop (craw), Icelandic kroppr (hump, bunch). Doublet of crop and croup.

Pronunciation

  • enPR: gro͞op, IPA(key): /ɡɹuːp/
  • Rhymes: -uːp

Noun

group (plural groups)

  1. A number of things or persons being in some relation to one another.
  2. (group theory) A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
    • 1977, Roger C. Lyndon, Paul E. Schupp, Combinatorial Group Theory, Springer, page 192,
      Throughout this section, we shall assume the existence of finitely presented groups with unsolvable word problem.
    • 1992, Svetlana Katok, Fuchsian Groups, University of Chicago Press, page 112,
      In this chapter we give some examples of Fuchsian groups. The most interesting and important ones are the so-called “arithmetic” Fuchsian groups, i.e., discrete subgroups of PSL(2,R) obtained by some “arithmetic” operations. One such construction we have already seen: if we choose all matrices of SL(2,R) with integer coefficients, then the corresponding elements of PSL(2,R) form the modular group PSL(2,Z).
    • 2007, Zhong-Qi Ma, Group Theory for Physicists, World Scientific, page 277,
      In Chap. 4 the fundamental concepts on Lie groups have been introduced through the SO(3) group and its covering group SU(2).
  3. (geometry, archaic) An effective divisor on a curve.
  4. A (usually small) group of people who perform music together.
  5. (astronomy) A small number (up to about fifty) of galaxies that are near each other.
  6. (chemistry) A column in the periodic table of chemical elements.
  7. (chemistry) A functional group.
  8. (sociology) A subset of a culture or of a society.
  9. (military) An air force formation.
  10. (geology) A collection of formations or rock strata.
  11. (computing) A number of users with same rights with respect to accession, modification, and execution of files, computers and peripherals.
  12. An element of an espresso machine from which hot water pours into the portafilter.
  13. (music) A number of eighth, sixteenth, etc., notes joined at the stems; sometimes rather indefinitely applied to any ornament made up of a few short notes.
  14. (sports) A set of teams playing each other in the same division, while not during the same period playing any teams that belong to other sets in the division.
  15. (business) A commercial organization.

Synonyms

  • (number of things or persons being in some relation to each other): collection, set
  • (people who perform music together): band, ensemble
  • See also Thesaurus:group

Hypernyms

  • (in group theory): monoid

Hyponyms

Derived terms

  • subgroup

Related terms

Descendants

  • Gulf Arabic: قروب
  • Japanese: グループ (gurūpu)
  • Korean: 그룹 (geurup)
  • Tongan: kulupu

Translations

References

  • group on Wikipedia.Wikipedia

Verb

group (third-person singular simple present groups, present participle grouping, simple past and past participle grouped)

  1. (transitive) To put together to form a group.
    group the dogs by hair colour
  2. (intransitive) To come together to form a group.

Synonyms

  • (put together to form a group): amass, categorise/categorize, classify, collect, collect up, gather, gather together, gather up; see also Thesaurus:round up
  • (come together to form a group): assemble, begather, foregather, throng; see also Thesaurus:assemble

Translations

Further reading

  • group in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
  • group in The Century Dictionary, New York, N.Y.: The Century Co., 1911.


English

Etymology

From French radical, from Late Latin rādīcālis (of or pertaining to the root, having roots, radical), from Latin rādix (root); see radix.

Pronunciation

  • enPR: rădʹĭk-əl, IPA(key): /ˈɹædɪkəl/
  • Homophone: radicle

Adjective

radical (comparative more radical, superlative most radical)

  1. Favoring fundamental change, or change at the root cause of a matter.
  2. (botany, not comparable) Pertaining to a root (of a plant).
  3. Pertaining to the basic or intrinsic nature of something.
    • 1790, Edmund Burke, Reflections on the Revolution in France
      The most determined exertions of that authority, against them, only showed their radical independence.
    Synonym: fundamental
    Antonyms: ignorable, trivial
  4. Thoroughgoing; far-reaching.
  5. (lexicography, not comparable) Of or pertaining to the root of a word.
  6. (phonology, phonetics, not comparable, of a sound) Produced using the root of the tongue.
    Coordinate terms: coronal, dorsal, labial, laryngeal
  7. (chemistry, not comparable) Involving free radicals.
  8. (mathematics) Relating to a radix or mathematical root.
  9. (slang, 1980s & 1990s) Excellent; awesome.

Synonyms

  • (linguistics, in reference to words): primitive

Antonyms

  • (linguistics, in reference to words): derivative, derived

Derived terms

Related terms

Translations

Noun

radical (plural radicals)

  1. (historical, 19th-century Britain) A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).
  2. (historical, early 20th-century France) A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.
  3. A person with radical opinions.
  4. (arithmetic) A root (of a number or quantity).
  5. (linguistics) In logographic writing systems such as the Chinese writing system, the portion of a character (if any) that provides an indication of its meaning, as opposed to phonetic.
  6. In Semitic languages, any one of the set of consonants (typically three) that make up a root.
  7. (chemistry) A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.
  8. (organic chemistry) A free radical.
  9. (algebra, commutative algebra, ring theory, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or





    I




    {\displaystyle {\sqrt {I}}}

    , such that an element xR is in Rad(I) if, for some positive integer n, xnI; equivalently, the intersection of all prime ideals containing I.

  10. (algebra, ring theory, of a ring) Given a ring R, an ideal containing elements of R that share a property considered, in some sense, “not good”.
  11. (algebra, ring theory, of a module) The intersection of maximal submodules of a given module.
  12. (number theory) The product of the distinct prime factors of a given positive integer.

Derived terms

Related terms

  • nilradical

Translations

References

  • radical in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
  • radical in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
  • “radical” in Raymond Williams, Keywords (revised), 1983, Fontana Press, page 251.

Further reading

  • Radical on Wikipedia.Wikipedia
  • Radical of an ideal on Wikipedia.Wikipedia
  • Radical of a ring on Wikipedia.Wikipedia
  • Radical of a module on Wikipedia.Wikipedia
  • Radical of an integer on Wikipedia.Wikipedia
  • Radical of an ideal on Encyclopedia of Mathematics
  • Ideal Radical on Wolfram MathWorld

Anagrams

  • aldaric, cardial

Catalan

Pronunciation

  • (Balearic, Central) IPA(key): /rə.diˈkal/
  • (Valencian) IPA(key): /ra.diˈkal/

Adjective

radical (masculine and feminine plural radicals)

  1. radical

Derived terms

  • radicalment
  • radicalisme
  • radicalitzar

Noun

radical m or f (plural radicals)

  1. radical

Further reading

  • “radical” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.
  • “radical” in Gran Diccionari de la Llengua Catalana, Grup Enciclopèdia Catalana.
  • “radical” in Diccionari normatiu valencià, Acadèmia Valenciana de la Llengua.
  • “radical” in Diccionari català-valencià-balear, Antoni Maria Alcover and Francesc de Borja Moll, 1962.

French

Etymology

Borrowed from Late Latin rādīcālis.

Pronunciation

  • IPA(key): /ʁa.di.kal/
  • Rhymes: -al
  • Homophones: radicale, radicales

Adjective

radical (feminine singular radicale, masculine plural radicaux, feminine plural radicales)

  1. radical

Noun

radical m (plural radicaux)

  1. (linguistics, grammar) radical, root

Further reading

  • “radical” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Galician

Pronunciation

Noun

radical m (plural radicais)

  1. radical (in various senses)

Derived terms

  • radicalismo
  • radicalizar
  • radicalmente

Further reading

  • “radical” in Dicionario da Real Academia Galega, Royal Galician Academy.

Portuguese

Pronunciation

  • Hyphenation: ra‧di‧cal
  • Rhymes: -al, -aw

Noun

radical m (plural radicais)

  1. (linguistic morphology) root (primary lexical unit of a word)
    Synonym: raiz

Noun

radical m, f (plural radicais)

  1. radical (person holding unorthodox views)
    Synonym: extremista

Adjective

radical m or f (plural radicais, comparable)

  1. radical (favouring fundamental change)
  2. drastic; extreme
  3. (Brazil, slang) excellent; awesome; thrilling
  4. (sports) extreme (dangerous)

Derived terms

  • radicalismo
  • radicalizar
  • radicalmente

Further reading

  • “radical” in Dicionário Priberam da Língua Portuguesa.

Romanian

Adjective

radical m or n (feminine singular radicală, masculine plural radicali, feminine and neuter plural radicale)

  1. radical

Declension

Related terms

  • radicalist
  • radicaliza

Spanish

Etymology

From Latin rādīcālis or Latin rādīx + Spanish suffix -al.

Pronunciation

  • IPA(key): /radiˈkal/, [ra.ð̞iˈkal]
  • Hyphenation: ra‧di‧cal

Adjective

radical (plural radicales)

  1. radical, seismic

Derived terms

  • radicalismo
  • radicalizar
  • radicalmente

Noun

radical m (plural radicales)

  1. radical

Derived terms

Further reading

  • “radical” in Diccionario de la lengua española, Vigésima tercera edición, Real Academia Española, 2014.

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